Volume and Surface Area of Rectangular Prisms Worksheet | 7th ... - Free Printable

To solve the problem of finding the volumes of the given objects, we need to calculate the volume of each individual shape and then combine them as necessary. The volume of a cuboid is calculated using the formula:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Let's solve each part step by step.

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1)

The object consists of two separate cuboids:
- Cuboid 1: Dimensions are \(4 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).
- Cuboid 2: Dimensions are \(2 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).

#### Volume of Cuboid 1:
\[
V_1 = 4 \times 2 \times 2 = 16 \, \text{cm}^3
\]

#### Volume of Cuboid 2:
\[
V_2 = 2 \times 2 \times 2 = 8 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 16 + 8 = 24 \, \text{cm}^3
\]

Answer for 1): \(\boxed{24}\)

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2)

The object is a larger cuboid with a smaller cuboid removed from it.
- Larger Cuboid: Dimensions are \(6 \, \text{cm} \times 6 \, \text{cm} \times 4 \, \text{cm}\).
- Smaller Cuboid: Dimensions are \(4 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).

#### Volume of Larger Cuboid:
\[
V_{\text{large}} = 6 \times 6 \times 4 = 144 \, \text{cm}^3
\]

#### Volume of Smaller Cuboid:
\[
V_{\text{small}} = 4 \times 2 \times 2 = 16 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_{\text{large}} - V_{\text{small}} = 144 - 16 = 128 \, \text{cm}^3
\]

Answer for 2): \(\boxed{128}\)

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3)

The object consists of three separate cuboids:
- Cuboid 1: Dimensions are \(5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Cuboid 2: Dimensions are \(3 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Cuboid 3: Dimensions are \(3 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).

#### Volume of Cuboid 1:
\[
V_1 = 5 \times 3 \times 2 = 30 \, \text{cm}^3
\]

#### Volume of Cuboid 2:
\[
V_2 = 3 \times 3 \times 2 = 18 \, \text{cm}^3
\]

#### Volume of Cuboid 3:
\[
V_3 = 3 \times 3 \times 2 = 18 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_1 + V_2 + V_3 = 30 + 18 + 18 = 66 \, \text{cm}^3
\]

Answer for 3): \(\boxed{66}\)

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4)

The object consists of two separate cuboids:
- Cuboid 1: Dimensions are \(4 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm}\).
- Cuboid 2: Dimensions are \(2 \, \text{cm} \times 2 \, \text{cm} \times 3 \, \text{cm}\).

#### Volume of Cuboid 1:
\[
V_1 = 4 \times 3 \times 3 = 36 \, \text{cm}^3
\]

#### Volume of Cuboid 2:
\[
V_2 = 2 \times 2 \times 3 = 12 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 36 + 12 = 48 \, \text{cm}^3
\]

Answer for 4): \(\boxed{48}\)

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5)

The object consists of two separate cuboids:
- Cuboid 1: Dimensions are \(5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Cuboid 2: Dimensions are \(3 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).

#### Volume of Cuboid 1:
\[
V_1 = 5 \times 3 \times 2 = 30 \, \text{cm}^3
\]

#### Volume of Cuboid 2:
\[
V_2 = 3 \times 3 \times 2 = 18 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 30 + 18 = 48 \, \text{cm}^3
\]

Answer for 5): \(\boxed{48}\)

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6)

The object is a larger cuboid with a smaller cuboid removed from it.
- Larger Cuboid: Dimensions are \(8 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm}\).
- Smaller Cuboid: Dimensions are \(4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm}\).

#### Volume of Larger Cuboid:
\[
V_{\text{large}} = 8 \times 6 \times 6 = 288 \, \text{cm}^3
\]

#### Volume of Smaller Cuboid:
\[
V_{\text{small}} = 4 \times 4 \times 4 = 64 \, \text{cm}^3
\]

#### Total Volume:
\[
V_{\text{total}} = V_{\text{large}} - V_{\text{small}} = 288 - 64 = 224 \, \text{cm}^3
\]

Answer for 6): \(\boxed{224}\)

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Final Answers:

1. \(\boxed{24}\)
2. \(\boxed{128}\)
3. \(\boxed{66}\)
4. \(\boxed{48}\)
5. \(\boxed{48}\)
6. \(\boxed{224}\)